Coupled thermopiezoelectric behaviour of a one-dimensional functionally graded piezoelectric medium based on C–T theory
Bibliographic record
Abstract
In this article, the transient thermopiezoelectric behaviour of a one-dimensional (1D) functionally graded piezoelectric medium subjected to a moving heat source is investigated. The formulation is given based on the Chandrasekhariah and Tzou (C–T) generalized thermoelasticity theory to consider the details of energy transport in the material in comparison with the Lord–Shulman (L–S) generalized theory. All material properties are taken to vary exponentially along the length of the medium except for phase lags, the relaxation time, and the specific heat, which are taken to be constant. The governing partial differential equations are given in the three coupled fields of displacement, temperature, and electric potential based on the C–T theory. Using Laplace transform to eliminate the time dependency of the problem, an analytical method is presented to obtain the coupled fields in the Laplace domain. The solutions are then derived in time domain by employing the fast Laplace inversion technique. Numerical results are shown to display the effects of discontinuities on the temperature and stress distribution, non-homogeneity index and the phase-lag constants of heat flux and temperature gradient on the wave propagation of temperature and stress fields based on the dual-phase-lag model of the C–T. Furthermore, the results are compared between the C–T and L–S thermoelasticity theories. Finally, the results are validated with those reported in the literature.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".